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Questions tagged [abstract-algebra]

For questions about groups, rings, fields, vector spaces, modules and other algebraic objects. Associate with related tags like group-theory, ring-theory, modules, etc. to clarify which topic of abstract algebra is most related to your question and help other users when searching.

6
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1answer
143 views
+50

Special elements in the $C^*$ algebra $A \otimes \mathcal{K}$.

Context: Let $A$ be an ungraded (not necessarily unital) $C^*$ algebra. $\mathcal{K}$ space of compact bounded operators on an infinite separable graded Hilbert space $H=H_0 \oplus H_1$. Consider ...
24
votes
1answer
432 views
+100

Balls and Boxes

Three urns contain marbles. Each urn is large enough to hold all the marbles . The only operation allowed is to move marbles from an urn to another urn, such that the number of marbles in the ...
3
votes
2answers
135 views
+50

What is the dicyclic group of order $12$? (What is $\mathbb{Z}_3\rtimes \mathbb{Z}_4$)

I have come across the dicyclic group of order $12$. I can see that this is generated by three elements subject to some relations. Is there a way to realize this group without talking about generators ...
5
votes
0answers
64 views
+50

Bounding the number of certain (translation) subsets in $\mathbb N \times \mathbb N$ with respect to given subsets

Let $\mathbb N = \{0,1,2,\ldots\}$ be the monoid of natural numbers with zero. Suppose $S \subseteq \mathbb N \times \mathbb N$ be some subset such that the number of sets of the form $\{ (i,j) \mid (...
1
vote
0answers
51 views
+50

Prime ideals of $R[x]$ that intersect $R$ in $P$

Let $R$ be a noetherian ring and $P$ a prime ideal of height $h$. Show that the prime ideals $Q\subset R[x]$ that intersect $R$ in $P$ are of the following two kinds, with height as shown: $Q=...
1
vote
2answers
52 views
+50

Can Rings be viewed as “function rings over their spectrum”?

In the nlab article about localization, a side note says When interpreting a ring under Isbell duality as the ring of functions on some space $X$ (its spectrum), […] Unfortunately, the article ...